You would never call Sally Potter a ginge. Not just because you wouldn't dare. Or because it would be like squirting ketchup over a slice of Poilane, or programming a double bill of The Tango Lesson and StreetDance 2 3D. You wouldn't even risk "strawberry blonde". The famed Potter mane is a big mingle of lemon and silver and cinnamon, which shimmers, Titian-ish.

Yet there is little doubt that she is, in some sense, Ginger, the carrot-topped hero of her new film. Ginger & Rosa is about baby-boomer best buddies, born on the same day, whose friendship in postwar London comes under strain when Rosa (Alice Englert) starts shagging Ginger's glamorous academic dad (Alessandro Nivola), freshly separated from her housewife mum (Christina Hendricks, doing downtrodden). The plot might not be autobiography, but Ginger's activist roots, social conscience, poetic heart, and parts of that barnet, are all Potter.

"Every story to some degree has to draw on personal experience," she says. "Magpie-like, you scavenge, and then you transform until it is its own world. But I did grow up during the Cuban missile crisis. I was on Aldermaston marches from the age of 10, I was very, very aware of the nuclear threat and I grew up in a leftwing, outsider, academic milieu. But it's a fiction."

In fact the friends are meant to be 16 going on 17, but the actor who plays Ginger, Elle Fanning, picking up much-deserved Oscar buzz, was just 13 at the time of the shoot – as was Potter in 1962. Ginger is riven with worry about the threat of annihilation; a threat the film is careful to justify, if not quite vindicate.

"I dreamed about it most nights," says Potter. "I had recurring nightmares. There'd be three minutes' warning and what could I do to save people, running hither and thither? Now we've got a much more creeping feeling of world destruction through climate change and so on. Not that feeling of imminent total doom. And it wasn't that long since the second world war. So there was a handed-down sense of apocalypse."

She coped by casting off inertia. "Fear is essentially a state of paralysis. As soon as you become active, you feel as if you're transforming your fear." So it's not so much about altruism? "No, more a feeling of connectedness with something broader and wider. The assumption that you can do something, paradoxically, takes a lot of confidence, even if that confidence is mixed in with fear and apprehension."

Potter is all about direct action. She left home at 16 to take backroom jobs at the BBC while making shorts as part of the London Film-Makers' Co-op. "I thought I was adult at 14. Looking back, I can see how vulnerable I must have been."

In the flesh, she seems composed, politely forthright. She sits in front of the window at her studio, all plants and art, wood floor and grand piano, at the top of a short tower block in Hoxton, east London. The floor below houses her production company's offices. Above, pigeons hop across the roof, which sounds as if it is made of tin. The creaks, the view, the dinky mezzanine, suggest a bohemian stateroom in a slightly rickety ocean liner.

Her films sport proud Potter thumbprints, from her debut, the all-female historical rewrite The Gold Diggers (1983), in which the star, Julie Christie, was paid the same as the lowliest gaffer, to I am an Ox, I am a Horse, I am a Man, I am a Woman (1988), a documentary about female practitioners of Soviet cinema. They are as uncompromising as their author, the same mix of thoughtful and flamboyant; high-strung tub-thumpers, always bracing, rarely boring.

But by far her biggest hit was 20 years ago: Orlando, an adaptation, starring Tilda Swinton, of the Virginia Woolf novel about a woman who flipflops through time and gender. Right through her career, Potter has snagged some surprisingly big names, yet even the likes of 2000's The Man Who Cried, with Johnny Depp, Cate Blanchett and Christina Ricci, was moderately received. Then came Yes (2003), a multicultural romance in iambic pentameter. Then Rage (2009), a digital, mostly monologue murder mystery with Jude Law and Judi Dench; the UK's first mobile-phone premiere.

"It didn't do quite what I wanted to do. It stumbled through the gate," she says. "So I then wanted to do something that was not obsessed with its form." And it is Ginger & Rosa's lack of self-consciousness, despite its personal origins, that makes it by far her most mainstream to date. The canvas has been opened out – she has recruited Robbie Ryan, Andrea Arnold's cinematographer – and the pace is kept snappy, thanks perhaps to new editor Anders Refn (Lars von Trier's longtime colleague, father of Nicolas Winding).

It is a film of warmth, even naivety. Spending so much time with her young stars was very affecting, says Potter. "The depth of relationship you go into – it's more intense than any other process that I know; it completely transcends gender, age, nationality. You have to leapfrog over those things and connect in a very, very deep way. When I see teenage girls walking around now, I feel very loving towards them and their struggles." Does she ever approach them? "No, but my hugs for my goddaughters were possibly extra-specially strong."

Ginger & Rosa distils the intensity of young friendship, and its covert, almost romantic secrecies. "There were very few spaces you could talk about the big things," she says, remembering her own nostalgically, "so you ended up sitting on the end of a bath with the door locked looking in the mirror and talking about the bomb or whatever." She feels the legitimate concerns of the young can still be belittled. "I think there's a terrible over-psychologising of people's anxiety. Maybe it's the children who are really awake? People talk about the tyranny of children – I think that's rubbish. You can still be capable of insight and you're certainly worthy of respect."

Yet Potter is at pains to be optimistic. "It was so glorious to see how much Occupy had learned from all these previous political movements. To have a free university tent, a therapy tent, the food, the safety patrols, equal rights of speaking at assembly! This microcosm of an ideal world concept. Absolutely brilliant. Fantastically good. It's always best to have a philosophical position of hope and therefore that activism is worthwhile."

There are many reasons Ginger & Rosa seems likely to go down better with the public than some of her previous films. One, which may be overshadowed by Fanning's almost frightening ability, is Nivola's turn as Ginger's father, Roland, the former conscientious objector baffled by the liberal ire in the face of his new relationship. Other characters have arcs; Roland has contradictions. On the one hand he justifies the affair as political action fighting mindless obedience: "I've broken the rules, all the rules, because someone has to say no." On the other, he protests that love must be simply surrendered to.

Potter sympathises. "Falling in love is a kind of madness. People feel that the feeling is hugely significant, as if it is beyond the rational or kindness or anything."

But how do his two arguments square? She pauses. "I think for a lot of the extreme rationalists there was an enormous dose of romanticism, too. They're wrestling with their own self-image. People draw a portrait of themselves that often leaves out the key thing, which inadvertently reveals what they really are or what they can't face in themselves."

Maybe Ginger, then, is a red herring. Potter, like Roland, does a lot of wrestling with the personal and the political. Her career has, in some ways, been a succession of self-portraits, but she made a bonafide two-minute one back in 2007, shot in an insomniac fog, then posted on her blog. Woozy footage of her face with no makeup, pot plants, computer, cooker, gets a knackered, fretful voiceover. "My mind says: Get up Sally, it doesn't matter if you're tired." It goes on, audio distorting. Then, at the end, it says: "And there's this guy …" Potter is not afraid to reveal key things, even if they are unappealing.

• Ginger & Rosa is released in the UK on 19 October

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